The curse of three dimensions: Why your brain is lying to you

Susan VanderPlas

07/24/2014

Outline

Biology

Why evolution doesn’t prefer statisticians

The Sine Illusion

Three Dimensions? Or Two?

Statistical Graphics

Quantifying the brain-paper divide experimentally

Conclusions

Knowing is half the battle

Biology

Perception is three-dimensional

Perception is three-dimensional

plot of chunk mullerlyer

Graphics are two-dimensional

Perception is three-dimensional

Ambiguous Figures


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Artistic Trickery



The Sine Illusion

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Three Dimensional Context

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Example: US Gas Prices


US Gas prices from 1995 to 2014 steadily increase over the time frame, with some dramatic short-term changes.

Example: US Gas Prices


Standard deviation of daily gas prices between 1995 and 2014. The doubling of the standard deviation over the time frame is masked in the scatterplot of the data

Understanding the Illusion

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We can correct the illusion by increasing the blue line’s length until the red line is equal to the actual distance



How much is your brain lying to you?

Tufte’s Lie Factor


\[ \text{Lie Factor} = \frac{\text{size of effect shown in graphic}}{\text{size of effect shown in data}} \]

Psychological Lie Factor

\[ \text{Lie Factor (Brain) = \frac{\text{size of perceived effect}}{\text{size of effect shown in graphic}}} \]

Experiment Setup